To add to things said above.
When kids are aged around 1-2.5, some days and stages you just barely sit down and need to be watching child attentively all the time. They'll be tottering around and need to be walked, or pulling at plants on a shelf, trying to climb on work surfaces etc. It's exhausting. Are your DP retired and usually rest when they want? They can tag team a bit but it's still a lot.
Would they care for DC at your house or their house? If theirs, probably there's a bit of childproofing to be done - do they have pale carpets, china ornaments, nice furniture? If they watch child at your house, prepare to find it a bit weird that they're using your stuff, putting things in wrong place, seeing things you might prefer they didn't etc.
A big one - attitudes to discipline have changed a lot, even in a few decades. Now there's lots of emphasis on emotional and mental health and wellbeing, helping children express themselves, validating their anger and trying to help them with it etc - previous generations are way less sensitive to this stuff and often think it's namby pamby nonsense, think best way to deal with tantrums is laughing or ignoring them and so on.
The likely thing is that the nursery would have a very gentle and sensitive, conflict-resolution based approach to discipline, you'll mimic this a bit but wing it and lose patience sometimes because you're only human, your parents will not bother with the softly-softly stuff and resolve situations with chocolate biscuits. Probably also way more TV and maybe phone or tablet time than you would ideally like.
What do you actually want your DC's relationship with DP to be like, and what do they want? The more hours they do, the more they will be hands-on with things like discipline, potty training, shaping behaviours etc. I think being a GP is much nicer when it's about a short burst of full attention, being taken somewhere nice and doing something nice, a bit away from the everyday routine.
It would also interfere with your DP routine - say they get invited to lunch with friends, or want to go to an event - do they say no as they have your DC?
If you rely on DP and then one gets ill/injured etc it's extra bad as you have the stress of the health aspect plus stress of trying to find childcare at short notice.
Personally we had childminder from 12 months for 2 days, GP for one day, I did two days. It worked fine. Then 4.5 days at nursery from age 3 and GP started doing overnight babysitting sometimes or taking them for days out here and there. Now DC are primary school age and will go for the odd overnight or stay with DP a couple of days in school holidays.